Silverlight Client Object Model For Windows Phone

In SharePoint 2010,Silverlight Client Object Model was not supported for Windows Phone
But This is improved in SharePoint 2013
As Windows Phone 7.5 first creates an object of the Authenticator class or ODataAuthenticator
which were added to the SharePoint 2013 client object model for Microsoft Silverlight for Windows Phone. It then uses this object as the user’s credentials.
Read more in this msdn post